Please use this identifier to cite or link to this item: https://oar.tib.eu/jspui/handle/123456789/2901
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dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.eng
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.ger
dc.contributor.authorFarina, Alberto
dc.contributor.authorValdinoci, Enrico
dc.date.accessioned2016-03-24T17:37:03Z
dc.date.available2019-06-28T08:12:58Z
dc.date.issued2014
dc.identifier.urihttps://oar.tib.eu/jspui/handle/123456789/2901
dc.identifier.urihttp://dx.doi.org/10.34657/1778-
dc.description.abstractWe study bounded, entire, monotone solutions of the Allen-Cahn equation. We prove that under suitable assumptions on the limit interface and on the energy growth, the solution is 1D. In particular, differently from the previous literature, the solution is not assumed to have minimal properties. We think that this approach could be fruitful in concrete situations, where one can observe the phase separation at a large scale and whishes to deduce the values of the state parameter in the vicinity of the interface. As a simple example of the results obtained with this point of view, we mention that monotone solutions with energy bounds, whose limit interface does not contain a vertical line through the origin, are 1D, at least up to dimension 4.
dc.formatapplication/pdf
dc.languageeng
dc.publisherBerlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
dc.relation.ispartofseriesPreprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2024, ISSN 2198-5855-
dc.subjectPhase transitions
dc.subjectsymmetry results
dc.subjectlimit interface
dc.subject.ddc510
dc.title1D symmetry for semilinear pdes from the limit interface of the solution
dc.typereport-
dc.typeText-
dc.description.versionpublishedVersioneng
local.accessRightsopenAccess-
wgl.contributorWIASger
wgl.subjectMathematikger
wgl.typeReport / Forschungsbericht / Arbeitspapierger
dcterms.bibliographicCitation.journalTitlePreprint / Weierstraß-Institut für Angewandte Analysis und Stochastik-
local.identifier.doihttp://dx.doi.org/10.34657/1778-
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